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When and under which circumstances did Physics and Mathematics take separate routes?

Even though connections between Mathematics and Physics have been strong and prosperous at all times the methods, goals and education of practitioners of both disciplines have diverged. Is it possible to trace back points in history where mathematicians lost interest in problems and techniques from Physics, and identified different ones as more relevant to Mathematics disregarding considerations about their usefulness for understanding nature, or the other way around, where influential Physicists made conscious decisions not to pursue objectives that they considered unrelated to the physical world?

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    $\begingroup$ I recommend you include more details. For example, why do you think there is such a separation. I think it is not even settled if one of them belongs to the other or not. There is a belief, again for example, that physics is a part of geometry, this makes a possible separation non-sense. $\endgroup$ Mar 12 at 2:34
  • $\begingroup$ I think in general the separation between different branches of science is an interesting topic. It is clear that it really got underway in the 19th century. It is amusing (to me) that some mathematicians have a helminthologist in their academic genealogy and what we classify people as today is probably not how they thought of themselves. Faraday was certainly both a chemist and physicist but he probably just thought he was studying nature. His math would have meant he could not have passed a freshman physics class today or even 100 years ago. $\endgroup$
    – releseabe
    Mar 12 at 9:30
  • $\begingroup$ Has the separation not always existed, although different branches of maths were involved differently? Think of Diophantine equations which were a big deal in maths for centuries since antiquity but have no real application. Or much of the ancient number theory stuff, e.g. prime numbers were quite useless until modern cryptography. It seems to me that there were always large branches of maths that had no relation to physics or whose applications were found only much later. $\endgroup$ Mar 12 at 10:44
  • $\begingroup$ BTW when I studied physics, the first two years of the curriculum were virtually indistinguishable from the maths university curriculum and we sat through much the same lectures as the maths students, so I can't quite see that there's much separation today, although both disciplines have some fields that are less connected than others. $\endgroup$ Mar 12 at 10:49
  • $\begingroup$ I do not think this question has an authoritative answer. For one thing, there are still some areas of math and physics, where there is no agreement which of the two an area belongs. In this sense, the two branches of science still did not completely separate. On the other hand, one can point to the mathematical formalism (and Hilbert as the most prominent advocate). If one accepts the formalist viewpoint, math (unlike physics) is completely disjoint from the "real world." But not everybody subscribes to the formalism. $\endgroup$ Mar 12 at 12:07

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I do not think that there was a moment when they separated: that is a time T such that they were one before T and separate after. Mathematics apparently started as an independent discipline from physics. Look at the work of Aristotle titled "Physics" and the work of Lucretius (exposition of Leucippus/Democritus system). They belong to physics, and they are certainly very different from mathematics of that time.

Legendary Pythagoras was credited with discoveries in both physics (relation between the length of a string and the sound it produces) and mathematics (theorems in geometry and number theory).

The close merge was achieved in the work of Archimedes; he practiced both mathematics and physics, but still in his writings this separation is evident. He never confuses physical reasoning with mathematical proof. In fact in a famous passage of his "Method" he emphasizes this difference.

At the later times, the two things sometimes came closer together, sometimes separated. And this should not be obscured by the fact that sometimes these two lines of inquiry were practiced by the same people.

The closest merge probably happened in 18th and early 19th centuries, but still at that time there was pure mathematics and mathematical physics and experimental physics. (See the famous exchange between Fourier and Jacobi on the goals of science).

This situation persists even now, at the time of high specialization: there are still many people on the boundary practicing both physics and mathematics. And there are other people who are either physicists or mathematicians but not both.

So my conclusion is that there was no separation point: two sciences were separate from the beginning, but most of the time there was a close interaction between them.

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